Question

The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is ______.

Options

• R – {3, – 2}

• R – {–3, 2}

• R – [3, – 2]

• R – (3, – 2)

Answer 1

The domain of the function f given by f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)` is R – {3, – 2}.

Explanation:

Given that: f(x) = `(x^2 + 2x + 1)/(x^2 - x - 6)`

f(x) is defined if x² – x – 6 ≠ 0

⇒ x² – 3x + 2x – 6 ≠ 0

⇒ (x – 3)(x + 2) ≠ 0

⇒ x ≠ – 2, x ≠ 3

So, the domain of f(x) = R – {– 2, 3}